Biomathematics and Statistics Scotland
Prediction of New Colonies – Seabird Tracking
Data (Under Agreement C10-0206-0387)
CONTRACT No: C10-0206-0387
Report submitted to:
Joint Nature Conservation Committee
November 2012
Authors:
Mark J Brewer, Jackie M Potts,
Elizabeth I Duff, David A Elston
CONTENTS
1.
2.
3.
4.
5.
6.
7.
PAGE
Non-Technical Summary
Introduction
Data
Methodology
Results
Prediction Maps of Usage
Discussion
3
4
6
14
17
29
42
In addition to this report, there are two further documents
associated with this project:
(i) BioSS Terns Report II – Results Appendix;
(ii) BioSS Terns Report II– Software;
and also ancillary files:
(i) Spreadsheet files of grid predictions for each of the
thirteen species/colony combinations for unsurveyed
colonies;
(ii) R code files for: ordination; fitting models to a
combination of sites; cross-validation; grid predictions
(iii) cleaned and standardised versions of the data files (for
survey data and grids).
This report is © Biomathematics and Statistics Scotland 2012
2
1. Non-Technical Summary
The Joint Nature Conservation Committee (JNCC) is working on the identification of important
marine areas around the UK that are used by five species of tern during the breeding season. For the
four larger tern species (Arctic, common, roseate and Sandwich terns), data are available from boat
surveys, using both visual tracking and transect survey methods.
Following a competitive tendering process, in June 2012 BioSS was tasked with making predictions
of usage and preference for Arctic, common and Sandwich terns for colonies lacking visual tracking
data.
This work forms part of Phase II of a larger tern project JNCC are undertaking, and follows on from a
previous project completed by BioSS earlier in 2012 as part of Phase I of the tern project. The Phase I
work we undertook previously used visual tracking data to learn about important associations between
terns’ usage/preference and environmental covariates, and to map usage/preference for each tern
species for those colonies with tracking data. The methodology developed from the Phase I project –
essentially a flexible weighted logistic regression model – would be used in this new, Phase II project.
Predictive models were defined for all new colonies which combined data from all relevant colonies
for each species separately. An evaluative procedure (employing assessment by a form of crossvalidation) determined that in terms of the colonies with data, better predictions were obtained by
combining data in this way rather than using ecological consideration or multivariate analysis of
environmental data to suggest subsets of “similar” colonies for prediction. As part of the crossvalidation analysis, we discovered that the most important predictors are distance to colony, distance
to shore, bathymetry and chlorophyll concentration.
Based upon the above analysis, predictions and prediction maps were produced for all requested
unsurveyed colonies.
3
2. Introduction
2.1 Background – Previous Phase
This project represents Phase II of analysis of data sets on four species of tern in several colonies in
UK offshore waters. Phase I was concerned with developing models specifically designed for the
type of tracking data available. The report for Phase I (Brewer et al., 2012) will be referred to
throughout this document as “the Phase I report”.
The Phase I analysis determined that a weighted logistic regression was appropriate for analysing the
data; the data itself was formed of individual tracks of known foraging instances (forming cases) with
sets of randomly generated perturbations of those tracks (forming controls). The analysis thus took a
case-control form. It was found that hierarchical (or random effect, mixed) models were not required,
as had been used in previous tracking analysis work by Aarts et al. (2008) and Wakefield et al. (2010)
– the difference being that for JNCC’s dataset, there were no known repeat observations per
individual. In this framework, the cases represent “presence” and the controls represent “absences”.
A number of explanatory variables were included in the regression, representing the environmental
conditions at different locations, but also including the measures “distance to colony” and “distance to
shore”.
Different forms of weighted logistic models were considered during Phase I analyses, using a range of
facilities in R. Both GLMs and GAMs were considered with various model selection strategies where
appropriate. Spatial autocorrelation of the response data was addressed, both by the weighting in the
regression and via a spatial correlation network derived using the INLA (Integrated Nested Laplace
Approximation) package in R (INLA, 2012). Different models were appropriate depending on the
purpose of the modelling – for example, whether the aim was to identify significant relationships with
the environmental covariates or to make predictions of usage and/or preference by each species in
each location.
Further details can be found in the Phase I report itself.
2.2 Second Phase – Colonies Without Tracking Data
JNCC wish to provide predictions for a number of colonies which have no tracking data available
(Phase II). The task at hand is to use data from surveyed colonies, using models such as those
developed in Phase I, to make predictions for these new colonies.
The new colonies as specified in the invitation to tender and subsequently modified by JNCC (with
agreement from BioSS) are the following (with colony names we shall use in the rest of this report in
bold):
4
Table 1. Colonies without tracking data available, for which predictions are to be made.
Common tern
Sandwich tern
Arctic tern
Dungeness
Foulness (Greater Thames)
Breydon Water (Norfolk)
Liverpool Bay (The Dee estuary; Ribble & Alt estuaries)
Strangford Lough (N Ireland)
Carlingford Lough (N Ireland)
Farne Islands (Northumberland)
Isle of May (Firth of Forth)
Liverpool Bay (Duddon Estuary)
Carlingford Lough (N Ireland)
Strangford Lough (N Ireland)
Strangford Lough (N Ireland)
Isle of May (Firth of Forth)
These colonies supplement the list of colonies in the Phase I report; however, we provide a list here of
colonies with data, as some new colonies (indicated with *) have been added for this Phase II work:
Table 2. Colonies with tracking data available.
Common tern
Sandwich tern
Arctic tern
Coquet and Farne* Islands (Northumberland)
Larne Lough (Northern Ireland)
Glas Eileanan / South Shian (Mull area, west Scotland)
Leith Docks (Firth of Forth)
Cemlyn (Anglesey)
Coquet and Farne Islands (Northumberland)
Larne Lough and Cockle* Island (Northern Ireland)
Sands of Forvie (Aberdeenshire)
Cemlyn (Anglesey)
Coquet and Farne Islands (Northumberland)
Copeland / Cockle Islands (Outer Ards, Northern Ireland)
The question of how to determine which of the colonies with survey data should be used to predict
which of the colonies without is addressed in the methodology Section 4. This required us to
determine suitable metrics for comparing models (within species) fitted using different subsets of
colonies and different selected covariates.
5
3. Data
3.1 Data Summary
The environmental covariates for this phase are as for the first part: see Section 2 of the Phase I report
for full details. As part of this second phase, we were required to conduct a deeper inspection of the
data in order to justify the “extrapolation” required in producing predictions and maps for the new
colonies. Boxplots were used to compare the ranges of the environmental covariates between
colonies; this is discussed in Section 4.2. Such differences in ranges were not of concern in Phase I as
each colony was analysed separately; only when multiple colonies are considered together is range
mismatch a potential problem.
Boxplots were also used to identify outliers and variables which have a skewed distribution. Section
3.2 which follows contains a discussion of outliers in some of the environmental variables; this
follows up a recommendation made by us in the discussion (Section 6) of the Phase I report. We also
considered whether we could use logged versions of chlorophyll concentrations and wave and current
shear stresses; on the basis of our new findings, we would recommend that this transformation could
have been applied during the Phase I analysis.
Some of the covariates considered in Phase I of the project were not considered further in Phase II.
Eastness, northness, slope and sand were not considered because they were not selected in any of the
Phase 1 models. (There was one exception where slope was selected by the AIC criterion, but was
not significant). The interannual standard deviation of probability of a frequent thermal front in
spring and summer were also excluded from the model selection process for Phase II. This was
because even though they were selected in some Phase I models, it did not seem biologically realistic
to suppose that the birds would respond to these variables while not responding to the probability of a
frequent thermal front itself. We would recommend excluding these from the Phase I models also.
3.2 Variable Inspection – Outliers
The boxplots in Figure 1 illustrate the range of values for each environmental covariate; as the
predictive grids for Sandwich (out to 55km from the colony) are different from those for the other
three species (out to 31km from the colony), there is a separate plot having only the colonies relevant
to Sandwich terns. The variable name is indicated by the y-axis, and the key for the colony codes on
the x-axis is as follows:
ce
co
fa
ll
le
mu
oa
br
ca
dn
fn
im
ri
Cemlyn
Coquet
Farnes
Larne Lough
Leith
Mull
Outer Ards
Breydon
Carlingford Lough
Dungeness
Foulness
Isle of May
Ribble
6
st
fo
du
Strangford Lough
Forvie
Duddon
The boxplots show a negatively skewed distribution for sea surface temperature, with low values
occurring near the shore. The extent to which these data are reliable is uncertain. Removal of the
values that were considered unreliable would have resulted in considerable loss of data, particularly
around the shore, so sea surface temperature was excluded from the analysis instead.
Chlorophyll concentrations and wave and current shear stresses had highly positively skewed
distributions and were therefore log-transformed prior to further analysis. (The log-transformed
versions are shown in the boxplots below). There was no reason to question the reliability of these, as
lognormal distributions frequently arise for variables such as chemical concentration which have low
mean values, high variances, and cannot be negative. On the other hand, some of the sea surface
temperature values, particularly those below 0C, seemed unrealistic.
7
Figure 1. Boxplots of environmental covariates. Colonies to the left of the vertical line are those
with tracking data and those to the right are those without.
8
9
10
11
12
13
4. Methodology
4.1 Weighted Logistic Regression via a Case-Control Design
As noted earlier, the form of statistical model used for analysing the tern tracking data was a weighted
logistic regression based on a case-control design. Full details of the modelling procedure and the
generation of the control data can be found in the Phase I report. We did not include INLA in Phase
II, as it was only used for model checking in Phase I and not for making predictions.
4.2 Comparisons of Environmental Data Between Colonies
One extremely important aspect of this project is to determine which colony or colonies can be used
to build models to make predictions for new colonies lacking tracking data. For each species, we
decided to compare the similarity or otherwise across colonies (or, more specifically, the foraging
ranges of colonies) of the environmental covariates used in the modelling. The reasoning for this is
that if a set of colonies appears to contain approximately the same environments, this might be
justification for using a model from one or more colonies within the set to obtain predictions for
another. On the other hand, colonies which are well-separated in multivariate environment space may
present radically different environments to terns, and therefore a model from one such colony may not
be suitable to predicting for another.
We compare the environmental data between colonies in two ways: firstly, we look at simple boxplot
summaries (presented in Section 3.2) for each environmental covariate in turn; secondly, we use a
principal component analysis (PCA) to study the combination of information from all covariates
simultaneously. Principal component analysis takes a set of variables and replaces them with a
smaller number of new variables (the principal components) in such a way that as much as possible of
the information in the original variables is retained in the new ones. This allows us to plot the data in a
concise way, for example by plotting the second principal component (PC2) against the first principal
component (PC1). Colonies which are close together in this plot will be similar in terms of the
original set of environmental covariates. This exploratory analysis will then help us in selecting
suitable subsets of colonies with which to build models for making usage and preference predictions
for the new colonies.
Visual inspection of the boxplots in Section 3.2 can indicate which variables may be unsuitable for
extrapolating from one colony to another. We found two such variables: (i) Salinity is a significant
covariate at Cemlyn, but the boxplots show that the distribution of salinity at Cemlyn is very different
from that at other colonies; (ii) wave and current shear stress are significant covariates at Outer Ards,
but the distribution of wave shear stress was different from that at many of the other colonies.
The set of variables to be considered in the PCA was:
bathy_1sec , strat_temp , summ_front , spring_front , log_chl_apr , log_chl_may ,
log_chl_june , log_ss_wave , log_ss_current , sal_spring , sal_summ.
However, some of the environmental variables are not available for some of the new colonies. For
example, at Dungeness ss_wave, ss_current, sal_spring and sal_summ are entirely missing. The PCA
function in R will remove entirely any row that contains a missing value; as such, trying to use all the
14
above variables can result in all data for one or more colonies being removed. The offending
variables are the final four in the set above; hence, for each species, we conduct a PCA both on the
above set of covariates (All Variables) and the following smaller set (Reduced Set of Variables):
bathy_1sec , strat_temp , summ_front , spring_front , log_chl_apr , log_chl_may ,
log_chl_june .
4.3 Cross Validation for Selecting Predictive Models for Colonies/Species
JNCC supplied us with suggested groupings for prediction purposes and were taken into consideration
in the cross-validation exercise. These are summarised briefly as follows and were based loosely on
geographical similarities. Some of these such as the close similarity between Coquet and Farne
Islands were confirmed by the PCA.
Table 3. Suggested colony groupings
Common tern
Group
1
2
3
4
5
6
Model
Coquet Island,
Farne Islands (very little data)
Coquet Island,
Farne Islands (very little data),
Cemlyn
Larne Lough
Prediction
Farne Islands,
Isle of May
Dungeness
Larne Lough
Cemlyn
Coquet Island,
Farne Islands,
Leith Docks
Larne Lough,
Glas Eileanan / South Shian (Mull),
Cemlyn
Strangford Lough,
Carlingford Lough
Strangford Lough,
Carlingford Lough
Foulness,
Breydon Water
Liverpool Bay (Ribble)
Arctic tern
Group
1
2
Model
Coquet Island,
Farne Islands
Outer Ards
15
Prediction
Isle of May
Strangford Lough
Sandwich tern
Group
1
2
Model
Larne Lough,
Cockle Island
Larne Lough,
Cockle Island,
Cemlyn
Prediction
Carlingford Lough,
Strangford Lough
Duddon Estuary,
Carlingford Lough,
Strangford Lough
The suggested ecological groupings and the PCA exercise indicated which colonies might be similar
in terms of environment and resulted in a series of colony groupings. Data from each colony within
each resulting grouping were combined to produce models that could be used to make predictions for
new colonies.
Cross-validation was used to select which colonies to use for prediction. This was done by assessing
the fit of predictions to the tracking data from a particular colony from (i) a model developed using
the remaining colonies in a proposed grouping and comparing this with (ii) a model developed using
data from all the remaining colonies. For example, it was suggested that data from Coquet and Farnes
might be used to predict Arctic terns at the Isle of May. We therefore tested whether Farnes was
better predicted using a model developed for Coquet alone, or a model using all available Arctic tern
data (Coquet and Outer Ards together). The assessment was carried out on the tracking data
(observations and controls) rather than on the grid data because we did not have presence-absence
data in the form of a grid.
Two scores were used to assess quality of predictions (fitted to the tracking data):
(1) The sum of squared errors
( y
i
 pi ) 2
If this quantity is divided by the number of observations, it gives the mean squared error, also known
as the Brier score when applied to probabilistic predictions (Brier, 1950);
(2) A score related to the log-likelihood
 ( y log( p )  (1  y ) log(1  p ))
i
i
i
i
where y is the binary variable indicating foraging behaviour and p is the predicted probability.
The intercept is arbitrary for case-control data as it depends on the ratio of controls to cases, which we
have chosen, and which has no biological meaning. An adjustment was therefore made to the
intercept for each model before calculating the two scores. A constant was added to the intercept to
ensure that the sum of the predicted probabilities was equal to the sum of the values of the binary
variable.
There are many other measures that could have been used; see Liu et al. 2011 for a review. For
example, the area under the receiver operating characteristic (ROC) curve, known as the AUC, is
widely used, although it has received some criticism (Lobo et al., 2008). It is unlikely that the overall
conclusions would have changed had we used a different metric – the results in the end were clear and
consistent in terms of prediction assessment, and predicted maps tended to vary only slightly for the
better-fitting models in any case.
Results and interpretation from this analysis are found in Section 5. The predictions themselves can
be found in supplemental spreadsheets while maps of predictions are presented in Section 6.
16
5. Results
5.1 Principal Component Analysis - Comparisons of Environmental Data
5.1.1 Common Tern – All Variables
With the full set of PCA variables, it can be seen that Farnes, Isle of May, Coquet and Leith all
occupy the same space in PC1 and PC2, suggesting that these colonies are similar in terms of the
major sources of variation in environmental conditions. Strangford and Carlingford Loughs appear to
lie between (but overlapping) Ribble and Larne Lough. Cemlyn seems to be something of an outlier
here, but note that there are a large number of missing values for the variable ss_current, which
removes most of the data points for that colony.
5.1.2 Common Tern – Reduced Set of Variables
With the reduced set of PCA variables, the picture changes dramatically. From the plot of PC2 vs
PC1, the colonies not seem to separate out at all well. The next plot – showing PC4 against PC3 –
shows that we need to go to the third principal component before we start getting clear colony
distinction. This in itself suggests that differences between colonies are not the major source of
17
variability in environmental conditions. In the PC4 vs PC3, the patterns are similar compared with
the plot in Section 5.1.1, but note that there are now more colonies included – those with all missing
values in the excluded variables. Interestingly, Dungeness seems to sit well with the Irish Sea
colonies, although we should stress again that from the PC2 vs PC1 plot, Dungeness does not appear
noticeably different from other colonies. In either plot, Foulness and Breydon seem similar to each
other; they resemble Ribble and Dungeness most closely in PC2 vs PC1, but are linked with Coquet in
PC4 vs PC3.
18
5.1.3 Sandwich Tern – All Variables
With the full set of PCA variables, we see that Coquet, Forvie and Farnes are similar, and that
Duddon overlaps Cemlyn. Larne Lough, Carlingford and Strangford lie in between these two groups.
19
5.1.4 Sandwich Tern – Reduced Set of Variables
With the reduced set of PCA variables, as with Common Terns we see a much less clear separation of
colonies. What we do see is that Duddon now overlaps Cemlyn very well, and that the Loughs Larne,
Strangford and Carlingford lie between Duddon/Cemlyn and Coquet/Farnes/Forvie.
20
5.1.5 Arctic Tern – All Variables
With the full set of PCA variables, there is very clear separation into groups. Coquet, Farnes and Isle
of May form one group, while Carlingford and Outer Ards form another. Cemlyn is something of an
outlier, but as noted for Common Terns, very many missing values for one variable means most
observations are deleted.
21
5.1.6 Arctic Tern – Reduced Set of Variables
With the reduced set of PCA variables, the group separation is less clear than with the full set, but still
apparent. Coquet, Farnes and Isle of May still overlap strongly, whereas Cemlyn, now less of an
outlier, overlaps Outer Ards. Carlingford Lough lies between these two overlapping groups.
22
5.2 Cross-Validation for Selecting Predictive Models for Colonies/Species
The aim was to find a set of variables that were consistent predictors across the different colonies for
which we have data, as it is more likely that these will be successful at making predictions for new
colonies. We took this approach, rather than considering all variables when selecting a model for a
combination of different colonies, because the latter approach would have tended to select variables
that explain a difference in intercept between colonies (which is of no interest), as well as those which
explain the pattern of foraging within a colony. In theory, as we have used a ratio of 12 controls to
each data point we would expect the intercept to be the same for each colony. However, in practice, it
differs because points have been excluded where control tracks fell on land and where there are
missing covariate values.
The variables that are consistently selected are dist_col, dist_shore, bathy_1sec and chl_june. When
considering models for combinations of sites in the cross-validation exercise the candidate variables
were reduced to this set. The variable that most commonly appeared to have a nonlinear effect in the
Phase I models was dist_col. We therefore considered GAM models with a nonlinear term in dist_col
as possible candidate models, but constrained the other terms to be linear.
23
Removal of some variables and log-transformation of others, as discussed in Section 3.2, led to some
changes in the models for single colonies developed in Phase I of the project. New models selected
using either AIC (Akaike’s Information Criterion) or likelihood ratio tests (LRT) are shown below.
This is to demonstrate that dist_col, dist_shore, bathy_1sec and chl_june were being selected
consistently; where AIC selects additional variables that are not on this list we present only the results
for LRT.
Arctic terns
Coquet: dist_col, chl_june, bathy_1sec (AIC and LRT)
Farnes: dist_col, dist_shore, sal_spring (AIC; LRT omits dist_shore)
Outer Ards: dist_col, chl_june, ss_wave, ss_current (AIC and LRT)
Common terns
Cemlyn: dist_col, bathy_1sec (AIC and LRT; salinity excluded)
Leith: dist_col, dist_shore, chl_may, chl_june, sal_summ (LRT)
Coquet: dist_col, bathy_1sec, chl_june (LRT)
Larne Lough: dist_col, dist_shore, chl_june, bathy_1sec (LRT)
Sandwich terns
Cemlyn: dist_col, dist_shore, chl_apr, chl_june (AIC; LRT omits dist_shore and chl_june)
Coquet: dist_col, dist_shore (LRT)
Farnes: dist_shore, sum_front, spring_front, bathy_1sec, sal_summ (AIC)
Forvie: dist_shore, strat_temp (AIC and LRT)
Larne Lough: dist_col, dist_shore (LRT – after excluding covariates with large numbers of missing
values)
Cockle Island: dist_col, chl_june, ss_current (AIC and LRT)
Cross-validation results are shown in Table 4 below. Note that due to the large number of missing
chlorophyll values for Larne Lough, chlorophyll was excluded when making predictions for Larne
Lough, and from any models in which Larne Lough is the sole colony used to make the predictions.
In general, predictions are better when data from all available colonies for that species are combined.
There are some cases where predictions based on a single colony are slightly better than those based
on all colonies combined, but they can be considerably worse. In the final models we have therefore
chosen to use data from all available colonies for each species, to provide a consistent approach. The
use of GAM models with a non-linear term for distance to colony sometimes makes predictions worse
when the model is applied to another colony. Chakraborty et al. (2011) note in general that GAMs
can be poor for out-of-sample prediction. Linear terms only were therefore used in the final
predictive models.
24
The following covariates were used for each species in the final models:
Arctic terns: distance to colony and bathymetry
Common terns: distance to colony, distance to shore and bathymetry
Sandwich terns: distance to colony, distance to shore, bathymetry and June chlorophyll concentration.
(June chlorophyll concentration was omitted for Strangford and Carlingford Loughs due to the large
number of missing values).
Full details of the models are presented in the Results Appendix.
25
Table 4. Results of cross-validation. Models with lower values of the sum of squared errors and higher values (i.e. lower absolute values) of the LL
score are better; the best model in each case is shown in bold type. The notation s(dist_col) indicates a GAM with a nonlinear term in distance to
colony.
Species
Colony to
predict
Model developed for
Covariates
LL Score
Arctic
Coquet
Arctic
Farnes
Common
Coquet
Farnes
Farnes, Outer Ards
Coquet
Coquet
Coquet, Outer Ards
Coquet, Outer Ards
Cemlyn
Leith
Leith
Cemlyn, Leith, Larne Lough, Mull, Farnes
Cemlyn, Leith, Larne Lough, Mull, Farnes
Cemlyn, Leith, Larne Lough, Mull, Farnes
Coquet
Coquet
Larne Lough
Coquet, Leith, Farnes
Coquet, Leith, Farnes
Coquet, Leith, Larne Lough, Mull, Farnes
Coquet, Leith, Larne Lough, Mull, Farnes
Coquet
Coquet
Coquet, Cemlyn, Farnes
Cemlyn, Coquet, Larne Lough, Mull, Farnes
Cemlyn, Coquet, Larne Lough, Mull, Farnes
dist_col
dist_col, bathy_1sec
dist_col, chl_june, bathy_1sec
s(dist_col), bathy_1sec, chl_june
dist_col, chl_june, bathy_1sec
dist_col, bathy_1sec
dist_col, bathy_1sec
dist_col, dist_shore, chl_may, chl_june, sal_summ
dist_col, chl_june
dist_col, bathy_1sec
dist_col, bathy_1sec, dist_shore
s(dist_col), bathy_1sec
dist_col, bathy_1sec, chl_june
s(dist_col), bathy_1sec, chl_june
s(dist_col), bathy_1sec, dist_shore
dist_col, bathy_1sec, chl_june, dist_shore
s(dist_col), bathy_1sec, dist_shore
dist_col, bathy_1sec, dist_shore
dist_col, bathy_1sec, chl_june, dist_shore
dist_col, bathy_1sec, chl_june
s(dist_col), bathy_1sec, chl_june
dist_col, bathy_1sec, chl_june
dist_col, dist_shore, bathy_1sec
s(dist_col), bathy_1sec
-9612
-9560
-4641
-4770
-4297
-4132
-7657
-5979
-5868
-6165
-6108
-6123
-3026
-3021
-4497
-3213
-3325
-3331
-3324
-16574
-16091
-17024
-14806
-14761
Cemlyn
Leith
26
Sum of
Squared
Errors
2582
2558
1306
1332
1217
1180
1970
1749
1744
1769
1761
1772
916
929
1326
971
1049
1007
1004
4514
4422
4627
4139
4134
Larne Lough
Sandwich
Larne Lough
Cemlyn
Cockle
Island
Cemlyn
Coquet, Farnes, Leith, Mull
Cemlyn, Coquet, Leith, Mull, Farnes
Cemlyn, Coquet, Leith, Mull, Farnes
Cockle Island
Cockle Island, Cemlyn
Cockle Island, Cemlyn
Cockle Island, Cemlyn, Coquet, Farnes, Forvie
Cockle Island, Cemlyn, Coquet, Farnes, Forvie
Larne Lough, Cockle Island
Larne Lough, Cockle Island, Coquet, Farnes, Forvie
Larne Lough, Cockle Island, Coquet, Farnes, Forvie
Cemlyn, Larne Lough
Cemlyn, Larne Lough, Coquet, Farnes, Forvie
27
dist_col, bathy_1sec
dist_col, bathy_1sec,dist_shore
dist_col, bathy_1sec,dist_shore
s(dist_col), bathy_1sec, dist_shore
dist_col, dist_shore
dist_col, dist_shore, bathy_1sec
s(dist_col), dist_shore
dist_col, dist_shore, bathy_1sec
s(dist_col), dist_shore, bathy_1sec
dist_col, bathy_1sec
dist_col,bathy_1sec,dist_shore
s(dist_col), dist_shore, bathy_1sec
dist_col,bathy_1sec,dist_shore,chl_june
dist_col,bathy_1sec,dist_shore,chl_june
-9214
-5034
-5046
-5185
-2692
-2523
-2942
-2063
-2250
-6742
-6729
-6606
-5990
-4760
1477
1373
1375
1415
794
736
879
595
697
2016
1834
1834
1387
1282
6. Prediction Maps of Usage
To calculate usage, preference is divided by distance to colony and multiplied by a scale factor which
ensures that the probabilities sum to one. For mapping purposes, the probabilities have been
multiplied by 1000. A very small number of points closest to the colony were removed if this gave a
value greater than 50.
Common Tern, Dungeness
28
Common Tern, Foulness
29
Common Tern, Breydon Water
30
Common Tern, Dee estuary
31
Common Tern, Ribble estuary
32
Common Tern, Strangford Lough
33
Common Tern, Carlingford Lough
34
Common Tern, Farne Islands
35
Common Tern, Isle of May
36
Arctic Tern, Strangford Lough
37
Arctic Tern, Isle of May
38
Sandwich Tern, Duddon estuary
39
Sandwich Tern, Strangford Lough
40
Sandwich Tern, Carlingford Lough
41
7. Discussion
Cross-validation has shown that it is generally better to combine all available data for a tern species
when making predictions for a new colony, rather than basing predictions on a colony or colonies that
appear to be ecologically similar. This means that the model developed for each species is more
robust, because it is based on data from a larger number of tracks, and covering a wider range of
environments. It might be possible to give the colonies differing weights, but it is unclear how such
weights should be chosen, as they would need to take account of the amount of data available for each
colony, as well as its ecological similarity to the colony being predicted which is difficult to measure
in relation to a terns assessment of its environment. The analysis has also shown that whereas the best
models for predicting the available data from a colony may involve many covariates and non-linear
terms, simple linear models with a small number of variables (in particular distance to colony,
distance to shore, bathymetry and chlorophyll concentration), are better for extrapolating to a different
colony.
42
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